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April 18th, 2010, 01:03 PM   #1
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Calculating Eigen Values error

Can someone find my error? The correct eigenvalues, if Matlab is to be believed, for the following matrix are -1, 1, 1, 1. I'm getting 1 and 0.


The only method I know so far for finding eigenvalues is to find the roots of the characteristic polynomial:


First substitute and subtract; second I added rows 2, 3, and 4 to row 1; third, factored out (1-lambda)


Next, expand along the first column; the first determinant is just the diagonal values multiplied:



Swap columns of the second determinant twice (col2<-->col3, then col1<-->col2 (doesn't change the value of the determinant -- well, it changes the sign twice) to make it diagonal and take the determinant by multiplying the values on the diagonal; then distribute:



The only roots of that last equation are:


I just re-rechecked my work as I was typing it in, too. Matlab, the back of my book, and my professor all say that the roots are 1 and -1 (and my professor doesn't like being asked any type of question which we should already know the answer to, like this one).

Thanks for your time and help.
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April 18th, 2010, 01:47 PM   #2
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Re: Calculating Eigen Values error

The determinant of the first 3x3 matrix should be not
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April 18th, 2010, 02:49 PM   #3
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Re: Calculating Eigen Values error

I missed that after looking over this problem about five times in the past two days?
Thanks!
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